44.77 Problem number 5746

\[ \int \frac {e^{\frac {x^3}{4+2 x+\log (2+x)}} \left (16+16 x+28 x^2+19 x^3+4 x^4+\left (8+4 x+6 x^2+3 x^3\right ) \log (2+x)+\log ^2(2+x)\right )}{16+16 x+4 x^2+(8+4 x) \log (2+x)+\log ^2(2+x)} \, dx \]

Optimal antiderivative \[ \left (2+x \right ) {\mathrm e}^{\frac {x^{3}}{\ln \left (2+x \right )+2 x +4}} \]

command

integrate((ln(2+x)**2+(3*x**3+6*x**2+4*x+8)*ln(2+x)+4*x**4+19*x**3+28*x**2+16*x+16)*exp(x**3/(ln(2+x)+2*x+4))/(ln(2+x)**2+(4*x+8)*ln(2+x)+4*x**2+16*x+16),x)

Sympy 1.10.1 under Python 3.10.4 output

\[ \text {Exception raised: TypeError} \]

Sympy 1.8 under Python 3.8.8 output

\[ \left (x + 2\right ) e^{\frac {x^{3}}{2 x + \log {\left (x + 2 \right )} + 4}} \]